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A097701
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Expansion of 1/((1-x)^2*(1-x^2)^2*(1-x^3)).
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6
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1, 2, 5, 9, 16, 25, 39, 56, 80, 109, 147, 192, 249, 315, 396, 489, 600, 726, 874, 1040, 1232, 1446, 1690, 1960, 2265, 2600, 2975, 3385, 3840, 4335, 4881, 5472, 6120, 6819, 7581, 8400, 9289, 10241, 11270, 12369, 13552, 14812, 16164, 17600, 19136
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..44.
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FORMULA
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a(n) = floor((n + 1) * (9*(-1)^n + n^3 + 17*n^2 + 95*n + 184)/288 + 1/2). - Tani Akinari, Oct 07 2012
a(0)=1, a(1)=2, a(2)=5, a(3)=9, a(4)=16, a(5)=25, a(6)=39, a(7)=56, a(8)=80, a(n)=2*a(n-1)+a(n-2)-3*a(n-3)-a(n-4)+a(n-5)+3*a(n-6)- a(n-7)- 2*a(n-8)+a(n-9). - Harvey P. Dale, May 20 2013
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MAPLE
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with(combstruct):ZL:=[st, {st=Prod(left, right), left=Set(U, card=r), right=Set(U, card<r), U=Sequence(Z, card>=1)}, unlabeled]: subs(r=5, stack): seq(count(subs(r=3, ZL), size=m), m=3..47) ; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 09 2007
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MATHEMATICA
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CoefficientList[Series[1/((1-x)^2(1-x^2)^2(1-x^3)), {x, 0, 50}], x] (* or *) LinearRecurrence[{2, 1, -3, -1, 1, 3, -1, -2, 1}, {1, 2, 5, 9, 16, 25, 39, 56, 80}, 50] (* Harvey P. Dale, May 20 2013 *)
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PROG
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(PARI) a(n)=1/576*(2*n^4+36*n^3+224*n^2+558*n+495+(18*n+81)*(-1)^n-64*(if(n%3, 1, 0)))
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CROSSREFS
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First differences of A002625. Partial sums of A008763.
Sequence in context: A138226 A175287 A007979 * A211881 A056870 A014739
Adjacent sequences: A097698 A097699 A097700 * A097702 A097703 A097704
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KEYWORD
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nonn
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AUTHOR
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Ralf Stephan, Aug 24 2004
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STATUS
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approved
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